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The MiniBooNE experiment at Fermilab has amassed the largest sample to dateof $\pi^0$s produced in neutral current (NC) neutrino-nucleus interactions atlow energy. This paper reports a measurement of the momentum distribution of$\pi^0$s produced in mineral oil (CH$_2$) and the first observation of coherent$\pi^0$ production below 2 GeV. In the forward direction, the yield of eventsobserved above the expectation for resonant production is attributed primarilyto coherent production off carbon, but may also include a small contributionfrom diffractive production on hydrogen. Integrated over the MiniBooNE neutrinoflux, the sum of the NC coherent and diffractive modes is found to be (19.5$\pm$1.1 (stat) $\pm$2.5 (sys))% of all exclusive NC $\pi^0$ production atMiniBooNE. These measurements are of immediate utility because they quantify animportant background to MiniBooNE's search for $\nu_{\mu} \to \nu_e$oscillations.

First Observation of Coherent $\pi^0$ Production in Neutrino Nucleus Interactions with $E_{\nu}<$ 2 GeV